Problem: What is the value of the following logarithm? $\log_{169} 13$
If $b^y = x$ , then $\log_{b} x = y$ Notice that $13$ is the square root of $169$ That is, $\sqrt{169} = 169^{1/2} = 13$ Thus, $\log_{169} 13 = \dfrac{1}{2}$.